Life history optimisation drives latitudinal gradients and responses to global change in marine fishes

Within many species, and particularly fish, fecundity does not scale with mass linearly; instead, it scales disproportionately. Disproportionate intraspecific size–reproduction relationships contradict most theories of biological growth and present challenges for the management of biological systems. Yet the drivers of reproductive scaling remain obscure and systematic predictors of how and why reproduction scaling varies are lacking. Here, we parameterise life history optimisation model to predict global patterns in the life histories of marine fishes. Our model predict latitudinal trends in life histories: Polar fish should reproduce at a later age and show steeper reproductive scaling than tropical fish. We tested and confirmed these predictions using a new, global dataset of marine fish life histories, demonstrating that the risks of mortality shape maturation and reproductive scaling. Our model also predicts that global warming will profoundly reshape fish life histories, favouring earlier reproduction, smaller body sizes, and lower mass-specific reproductive outputs, with worrying consequences for population persistence.

reproduction is indeed hyperallometric (2). (Lines,(17)(18) L 33-41: Please clarify what measure of reproductive output is being considered here. In addition, is intraspecific (ontogenetic) or interspecific (phylogenetic) body-mass scaling of reproduction being considered here? Interspecific scaling patterns of reproductive biomass are often isometric or hypoallometric, and rarely hyperallometric. For fishes, in particular, across species clutch mass scales nearly isometrically and clutch size scales hypoallometrically (see reviews by Blueweiss et al. 1978;Visman et al. 1996;Hendriks & Mulder 2008). Olsson & Gislason (2016) also report that reproductive output (g/yr) scales hypoallometrically in fishes. Note that references 1-3 cited by the authors do not provide comprehensive reviews of reproductive allometry in animals & plants, such as the ones that I mention above.
We now make clear that we are only considering reproductive output within species for fish.
We also mention instances when reproduction scales hypoallometrically with mass.  L 42-44: The papers cited (references 8-10) focus on intraspecific growth models, and do not clearly show how fecundity should scale with body mass across species. Furthermore, these models could be used to predict a variety of intraspecific scaling relationships for reproductive parameters, not just hyperallometry. The authors should make clear that these models do not explicitly predict interspecific fecundity scaling relationships, and at the intraspecific (ontogenetic) level may be used to predict a variety of scaling relationships. Overall, the specific papers that are cited do not unambiguously support the authors' statements about reproductive hyperallometry (see also specific comments regarding each study below): (8) Day & Taylor (1997): This commentary about intraspecific growth models makes no clear predictions about how fecundity should scale with body mass across species. Moreover, the fecundity model (equation 10) that is mentioned assumes a scaling exponent of 2/3 (see also specific comments).
Please refer to our response to point (9) below.. Kozlowski (1996): This study focuses only on species showing indeterminate growth. His model groups together growth and reproduction as "production", thus not allowing a specific prediction of how reproduction should change with body size. In his model, P is assumed to scale hypometrically with body mass. The idea that allocation to reproduction may increase with body size may make sense intra-specifically, at least in some cases, but how this would translate into interspecific scaling of reproduction is not explicitly explained. Also keep in mind that the proposed model is not general, as it does not apply to determinate growers.
We disagree with the reviewer that these models do not predict reproductive hyperallometry both models assume hypoallometric production but under all modelled conditions, the math yields hyperallometric scaling of reproduction within species (even if the text of these papers did not emphasise this result, the result was contained in the formal theory). We are specifically only interested in how fecundity scales with body within species, and how that scaling differs among species and hence these models are most relevant.
(10) Gadgil & Bossert (1970): In this study, changes in reproductive effort with age and body size are modelled for semelparous & iteroparous species. Although reproductive effort is predicted to increase with age in iteroparous species, their Figure 5 shows that they believe that offspring number should increase at a slowing rate or even eventually decrease after a peak is reached, as body size increases (as shown in trees: Qui et al. 2021). This represents hypoallometry, not hyperallometry. One should not confuse size with age. Furthermore, they make no specific predictions about how fecundity should scale with body size across species.
We've removed this paper as the reviewer makes a good point.
Lastly, the authors ignore the models discussed by Olsson & Gislason (2016) that predict hypoallometry of reproduction in fishes. Please explain. Olsson and Gislasson (2016) investigates the interspecific reproductive scaling of size at maturity, which they estimate to be hypoallometric (0.84). This reproductive scaling is different to the intraspecific scaling of reproduction with female mass, which is the focus of our study. Nevertheless, we now explicitly state that interspecific relationships between mass and reproduction are likely to differ from the intraspecific (and intrapopulation) patterns examined here. (Lines 116-120) L 57-59: Please explain why the cited models cannot predict variation in reproductive scaling.
We now say that we explicitly test the predictions of Day and Taylor and Kozlowski, that predict that life history (mortality and growth) should shape reproductive scaling. It would be necessary to include variation in production rate parameters, season length, etc. to get predictions on variation in reproductive scaling.

Done.
L 84-85: Please explain. How is "reproductive scaling" quantified? This vague term is frequently used in this manuscript.

We define reproductive scaling as the mass scaling of batch fecundity. (Lines 103-106)
L 98-104: These predictions seem to make the implicit assumption that intra-and interspecific fecundity scaling relationships are the same. In other words, the intraspecific relationship of a small species should directly extrapolate into the same relationship for a larger species. Given the diversity of intraspecific relationships, this assumption seems problematic to me and should be justified.
There seems to be a miscommunication here, we're only making predictions about how within-species fecundity scalings should vary among species -we don't make any predictions about among species fecundity scaling. We've tried to make this clearer in the revised ms.
Yes they are log-log slopes within species. We have clarified this.  L 109-112. A similar increase in egg size across all individuals and species would increase the elevation of the reproductive (total offspring volume vs number) scaling relationship, but not the slope. Please clarify.

Yes, we agree and we have now corrected this.
L 250-251: Actually, Day & Taylor (1997) assume that fecundity (not just production, P) scales to the 2/3-power (equation 10), which is contrary to the claim of the authors of the submitted manuscript that the model of Day & Taylor (1997) predicts reproductive hyperallometry. The authors should make clear that it is not only the mass-scaling of P that determines the scaling of fecundity, but also how the proportion of P that is allocated to growth changes with age (which they are well aware of). In doing so, however, changes in fecundity with age may not equate with changes in size, so it seems that predicting the scaling of fecundity is not completely straightforward (see also General Comment 3).
We agree with the reviewer that, upon first glance, Eq 10 in Day and Taylor gives the impression that fecundity scales at 2/3 with mass. However, changes in energy allocation from growth to fecundity also affect the scaling, causing hyperallometry. We recognise that readers familiar with the model of Day & Taylor (1997) might also have a similar confusion, so we now have a much more detailed exposition of how the change in energy allocation alters the scaling.  L 316: Change "use" to "used".

Done.
L 635-636: It would be helpful to specify that "reproductive scaling" (too vague) involves fecundity.
Throughout the manuscript, reproductive scaling is the slope of fecundity as a function of weight in log-log scale. We have made this clear now.